# Finite Difference Method

*Quant & Pricing — Finicade finance glossary*

The finite difference method prices derivatives by solving the pricing PDE numerically on a grid of price and time. It is the fastest accurate route for low-dimensional problems with early exercise, and it produces the Greeks almost for free as grid derivatives. Explicit schemes are simple but conditionally unstable; Crank-Nicolson is the usual production choice. Beyond three or four state variables the grid explodes and Monte Carlo takes over.

**Also known as:** PDE solver, Crank-Nicolson, explicit and implicit schemes

**Related terms:** [Black–Scholes PDE](https://finicade.com/glossary/black-scholes-pde), [Trinomial Tree](https://finicade.com/glossary/trinomial-tree), [Monte Carlo Simulation](https://finicade.com/glossary/monte-carlo), [Backward Induction](https://finicade.com/glossary/backward-induction), [American Option](https://finicade.com/glossary/american-options)

**Taught in:** Quant Quest — The PDE Approach

Source: https://finicade.com/glossary/finite-difference-method